The volunteers at the animal shelter are drawing slips of paper from a hat to determine which day each volunteer will clean the litter boxes. When it is Odessa's turn to pull from the hat, there are 2 Wednesday slips, 8 Thursday slips, and 6 Friday slips remaining. What is the probability that Odessa will randomly draw a Wednesday slip?

Answer:

$2 per pound.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know,

1 hour = 60 minutes

Therefore,

\( \frac{11}{4} hour =( 60 \times \frac{11}{4} )minutes\)

= 165 minutes (Ans)

Answer:

The two numbers are 8 and -2

Step-by-step explanation:

a=b+10

2(a+b)=12

you then substitute the first equation's value for a into the second equation.

2(b+10+b)=12

2(2b+10)=12

4b+20=12

b+5=3

b=-2

Then you substitute this value for b back into the first equation.

a=b+10

a=-2+10

a=8

It would take the toy car approximately 1.25 hours to travel 5 miles.

If a toy car can go at a speed of 4 mph, we can calculate the time it would take for the car to cover a distance of 5 miles.

To determine the time, we can use the formula:

Time = Distance / Speed

In this case, the distance is 5 miles and the speed is 4 mph. Plugging these values into the formula, we get:

Time = 5 miles / 4 mph

Dividing 5 by 4 gives us 1.25.

Therefore, it would take the toy car approximately 1.25 hours to travel 5 miles.

To understand this further, we can break down the calculations. In one hour, the toy car would cover a distance of 4 miles since it travels at a speed of 4 mph. For the remaining 1 mile, it would take an additional 0.25 hours (15 minutes) since the car is still moving at the same speed.

It's important to note that the calculation assumes a constant speed throughout the journey and doesn't account for factors such as acceleration, deceleration, or any potential obstacles. Also, keep in mind that this calculation is specific to the given speed of 4 mph. If the speed were to change, the time required to cover the distance would be different.

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\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

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Answer:

The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Step-by-step explanation:

The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2

Which gives;

3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0

3.1·x³ - 6.4·x²+ 3·x  - 5 = 0

Factorizing online, we get;

3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0

Therefore, the possible solutions are;

x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0

The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;

x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.

Answer:

40.4026226 aka 40.403

Step-by-step explanation:

tan 22 degrees = h/100

Where the above conditions exist,

The random variable T = L + C represents the total time it takes Lorelei and Chance to finish a randomly selected 3-layer wedding cake. Since L and C are independent and Normally distributed, T is also Normally distributed with mean:

Mu_T = Mu_L + Mu_C = 37 + 52 = 89

and variance:

Var(T) = Var(L) + Var(C) = 12^2 + 7^2 = 193

So the standard deviation of T is:

Sigma_T = sqrt(Var(T)) = sqrt(193) = 13.89

The shape of T is also Normally distributed, since it is a sum of two independent Normally distributed variables.

To find the probability that Lorelei and Chance finish a randomly selected 3-layer wedding cake in under 90 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table. The z-score is:

z = (90 - 89) / 13.89

= 0.072

From the z-table, we find that the probability of a Z-score less than or equal to 0.072 is 0.5287.

Therefore, the probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is 0.5287 or approximately 53%.

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Answer:

option 4

Step-by-step explanation:

-3.4x + 4.7 - (3 + 2.9x) = -3.4x + 4.7 - 3  - 2.9x  (combine like terms)

                                   = -3.4x - 2.9x + 4.7 - 3

                                  = - 6.3x + 1.7

If two number have same sign, add and put the common sign for the answer.

If two numbers have different sign, subtract and the answer will have the sign of the bigger number

Answer:

Route A is 0.75 km longer than route B.

Step-by-step explanation:

Length of route A is 1.5 times the length of route B.

a = 1.5b

\(\frac{a}{b}=\frac{15}{10}\)

\(\frac{a}{b}=\frac{3}{2}\) --------(1)

Here, a = Length of route A

b = Length of route B

Length of route A is \(\frac{3}{4}\) of route C.

a = \(\frac{3}{4}c\)

\(\frac{a}{c}=\frac{3}{4}\) ------(2)

Here, c = Length of route C

Length of route C = 3 km

Length of route A = \(\frac{3}{4}\times 3\) [From equation (2)]

                             = 2.25 km

Length of route B = \(\frac{2}{3}\times 2.25\) [From equation (1)]

                             = 1.5 km

Difference in route A and route B = 2.25 - 1.5

                                                       = 0.75 km

Therefore, route A is 0.75 km longer than route B.

The values of angle J and angle G are 32° and 78° respectively.

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to similar , the corresponding angles must be equal and also the corresponding sides must be equal.

Therefore since triangle HIJ is similar to triangle GEF, then

angle G = angle H

angle I = angle E

angle J = angle F

Therefore;

angle G = angle H = 78°

angle F = angle J = 32°

Therefore the values of angle J and angle G are 32° and 78° respectively.

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The heart rate increases gradually during the initial stages of exercise and then it increases sharply.

The graph represents a person’s heart rate in beats per minute during 30 minutes of exercise.

The best statement that describes the relationship between heart rate and time during exercise is that the heart rate increases gradually during the initial stages of exercise and then it increases sharply.

Heart rate (HR) is the number of heartbeats per unit of time, generally expressed as beats per minute (BPM), that an individual's heart pumps per minute (bpm).

The pulse is usually determined by evaluating arterial blood flow in any blood vessel that can be palpated near the surface of the skin at various points on the body (peripheral pulse).

Exercise is any physical activity that improves or sustains physical health, overall well-being, and/or athletic ability while also providing entertainment.

Exercise may be done on a regular basis, such as daily, or at a specific time, such as when athletes participate in athletic activities.

Exercise may be performed in a variety of settings, including health clubs, the outdoors, or one's own home.

Given the graph of a person's heart rate during 30 minutes of exercise, the heart rate is seen to increase gradually at the beginning of the exercise, then increase sharply before remaining constant for a short period before decreasing slowly over time.

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Answer:

The common ratio would be 8:1.            

Answer:

104.92

Step-by-step explanation:

Answer: 17

Step-by-step explanation:)

hi I don't know the answer

Hope you could understand.

If you have any query, feel free to ask.

Answer:

The volume of cylinder is 3416.32 in³.

Step-by-step explanation:

Given :

\(\begin{gathered}\end{gathered}\)

To Find :

\(\begin{gathered}\end{gathered}\)

Using Formulas :

\(\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}\)

\(\star{\small{\underline{\boxed{\sf{\pink{Volume_{(Cylinder)} =\pi{r}^{2}h}}}}}}\)

\(\begin{gathered}\end{gathered}\)

Solution :

Here we have given that the diameter of cylinder is 16 in. So, finding the radius of cylinder by substituting the values in the formula :

\({\longmapsto{\sf{Radius_{(Cylinder)} = \dfrac{D}{2}}}}\)

\({\longmapsto{\sf{Radius_{(Cylinder)} = \dfrac{16}{2}}}}\)

\({\longmapsto{\sf{Radius_{(Cylinder)} = \cancel{\dfrac{16}{2}}}}}\)

\({\longmapsto{\sf{Radius_{(Cylinder)} = 8 \: in}}}\)

\(\star\underline{\boxed{\sf{\red{Radius_{(Cylinder)} = 8 \: in}}}}\)

Hence, the radius of cylinder is 8 in.

\(\begin{gathered}\end{gathered}\)

Now, finding the volume of cylinder by substituting the values in the formula :

\({\longrightarrow{\sf{Volume_{(Cylinder)} =\pi{r}^{2}h}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times {(8)}^{2} \times 17}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times {(8 \times 8)}\times 17}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times {(64)}\times 17}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times 64\times 17}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} =200.96\times 17}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} =3416.32 \: {in}^{3}}}}\)

\(\star{\underline{\boxed{\sf{\red{Volume_{(Cylinder)} =3416.32 \: {in}^{3}}}}}}\)

Therefore, the volume of cylinder is 3416.32 in³.

\(\rule{300}{2.5}\)

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x=3

Step-by-step explanation:

Answer:

3.0

Step-by-step explanation:

In question 27, the price elasticity of supply for shampoo is given as 20, and the price of shampoo increases by 0.7%. The expected change in the quantity of shampoo supplied can be determined using the concept of price elasticity of supply. However, the specific percentage change in quantity supplied is not provided, so a precise answer cannot be given based on the given information.

In question 20, an inferior good in which the income effect dominates the substitution effect is referred to as a Giffen good. It is not classified as a normal good, luxury good, mass-produced good, or favored good.

In question 30, the cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of its substitutes and complements. The correct answer is that the cross elasticity of demand measures the responsiveness to changes in both substitutes and complements.

In question 27, without the specific percentage change in quantity supplied, we cannot determine the exact outcome based on the given information. The price elasticity of supply of 20 suggests that the quantity supplied is highly responsive to changes in price, but the specific percentage change in quantity supplied cannot be calculated without additional data.

In question 28, the relationship between pasta being a Giffen good and other characteristics is not specified. While pasta being a Giffen good indicates that the quantity demanded increases as the price increases, it does not imply whether pasta is a normal good, luxury good, or how price changes affect quantity demanded.

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Answer:

x=8.67698104181

Step-by-step explanation:

i got this answer using the pythagorean theorem

In a graph with 5 vertices, four vertices of degree 3 and one vertex of degree 2, the number of edges can be calculated using the Handshaking Lemma.

The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is twice the number of edges. In this case, we have four vertices of degree 3 and one vertex of degree 2. The sum of the degrees of these vertices is 4×3 + 2 = 14. According to the Handshaking Lemma, this sum is twice the number of edges. Therefore, we can solve the equation 14 = 2 ×E, where E represents the number of edges in the graph.

Solving this equation, we find that E = 7. So, the graph with four vertices of degree 3 and one vertex of degree 2 would have 7 edges.

Now let's consider the second question. The graph has 5 vertices and 10 edges. Two vertices are of degree 3, one vertex is of degree 2, and one vertex is of degree 5. To find the degree of the remaining vertex, we can again apply the Handshaking Lemma. The sum of the degrees of the known vertices is 3 + 3 + 2 + 5 = 13. According to the Handshaking Lemma, this sum is equal to twice the number of edges. So, we can solve the equation 13 = 2 × 10, where 10 represents the number of edges in the graph. Solving this equation, we find that it is not possible for the remaining vertex to have a degree of 0. Therefore, there must be an error in the given information, as it is not possible to have a graph with the specified degrees and number of edges.

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The third-degree polynomial function with real coefficients, having -9i, 9i, and 3 as zeros, can be expressed as f(x) = (x^2 + 81)(x - 3).

To form a third-degree polynomial function with real coefficients such that -9i and 3 are zeros, we need to consider the complex conjugate of -9i, which is 9i. Therefore, the zeros of the polynomial function are -9i, 9i, and 3.

A polynomial with real coefficients and given zeros will have factors that correspond to each zero. The factors for the given zeros can be expressed as follows:

(x - (-9i))(x - 9i)(x - 3) = 0

Simplifying this equation, we get:

(x + 9i)(x - 9i)(x - 3) = 0

Expanding the expression further:

(x^2 - (9i)^2)(x - 3) = 0

(x^2 + 81)(x - 3) = 0

Finally, multiplying the factors together, we obtain the third-degree polynomial function with real coefficients:

f(x) = (x^2 + 81)(x - 3)

This polynomial function satisfies the requirement of having -9i, 9i, and 3 as zeros and consists of real coefficients.

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Answer:  1 1/14

Step-by-step explanation: sorry if im wrong

It will take 56.2 years for Strontium-90 to decay to 25% of its initial quantity, when it has a half-life of 28.1 years.

The half life of an element is the time period in which it decomposes to half of itself.

The formula used is:

\(N(t) = N_0 (\frac{1}{2} )^{\frac{t}{t_{1/2} }}\),

where, N(t) is the final quantity of the element after time t, with the initial quantity was N₀, and \(t_{1/2}\) is the half life of that element.

In the question, we are given that Strontium-90 has a half-life of 28.1 years.

Thus, \(t_{1/2}\) = 28.1 years.

We are asked the time (t), it will take for a sample of Strontium-90 to decay to 25% of its initial quantity.

We assume the initial quantity to be N₀.

The final quantity N(t) is 25% of the initial quantity.

Thus, N(t) = 25% of N₀ = 25/100 * N₀ = N₀/4.

Substituting all the values in the formula, we get:

\(N(t) = N_0 (\frac{1}{2} )^{\frac{t}{t_{1/2} }}\\\Rightarrow N_0/4 = N_0(\frac{1}{2} )^{\frac{t}{28.1} }}\\\Rightarrow \frac{N_0/4}{N_0} = (\frac{1}{2} )^{\frac{t}{28.1} }}\\\Rightarrow \frac{1}{4} = (\frac{1}{2} )^{\frac{t}{28.1} }}\\\Rightarrow (\frac {1}{2})^2 = (\frac{1}{2} )^{\frac{t}{28.1} }}\\\Rightarrow \frac {t}{28.1} = 2\\\Rightarrow t = 28.1*2 = 56.2\)

Thus, it will take 56.2 years for Strontium-90 to decay to 25% of its initial quantity, when it has a half-life of 28.1 years.

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Answer:

56.2 years is correct for plato

Step-by-step explanation:

took the test

Considering the definition of vertex of a quadratic equation, the vertex of the quadratic equation y=5x²+30x+50 is (-3; 5).

A quadratic function is a variable of a polynomial function defined by f(x)=ax² + bx +c, where a≠0

The value of -b÷(2a) indicates the value of x of the vertex of the parabola.

Replacing this value into the function, you get the value of y of the vertex of the function.

In this case, the quadratic equation y=5x²+30x+50, where:

The value of x of the vertex is calculated as -30÷(2×5)

Solving:

x= -30÷10

x= -3

The value of y of the vertex of the function is calculated as y=5×(-3)²+30×(-3)+50

Solving:

y= 45 -90 +50

y= 5

Finally, the vertex of the quadratic equation is (-3; 5).

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The rounding of the number to 1 significant figure is-

216 × 876 = 180000

216 × 876

This number can be written in form of rounding to 1 significant figure as;

200 × 900 = 180000

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